Unlawful, informal exclusions are always unlawful.
Objecting to the EHCP includes when there is not sufficient funding to deliver the SEP detailed, specified and quantified.
The school CAN say they will have the child there for the 1:1 funded hours, but they will not have him there more than that.
This is objecting to the EHCP. The school would be objecting to being named when the EHCP does not include sufficient provision (in their opinion).
If this was not the case, then any child with an EHCP could go to ANY school or college they/their parents wanted, and the school would have to adapt to them, regardless of what those adaptions were.
OP’s situation is a different situation because the school is already named. The school must admit (they have) and cannot unlawfully informally exclude. However, LAs and SENDIST do not need the school’s agreement in order to be named unless the school is wholly independent. They can be named even if they object.
If what you're saying right, then suppose my child has an EHCP for PMLD - he needs access to a physio/hydro/sensory room/changing room with shower. From what you are saying the school would either have to PROOVE he didn't need any of those things, or have to build them, so he could attend.
I am saying if the EHCP for a child with PMLD named a MS, the MS would still have to admit and cannot unlawfully exclude.
It is irrelevant if the school think detailed, specified and quantified provision isn’t required. It must be provided and can be enforced. The school/LA not providing it leaves the LA and school open to legal action.